Spontaneous macroscopic

The advantages of SSFLC devices derive to a large extent from the spontaneous macroscopic polarization P of the phase. For example the electrooptic rise time of a prototypical SSFLC light valve is inversely proportional to the magnitude of the polarization. In order to design new FLC materials with large P in a directed way, we... 

In equilibrium, neither the forward reaction nor the backward reaction takes place spontaneously. Macroscopically speaking, there is no more transformation and the composition of the reaction mixture remains constant However, forward and backward reactions do continue to occur at the microscopic level between the particles. These happen at identical rates though, so that the transformations in the two directions compensate for each other. In this case, one speaks traditionally of a dynamic equilibrium, an equality of forward and backward forces although one means a kinetic equilibrium, an equality of forward and backward reaction rates. We will go into this in more detail later on in Sect. 17.2. 

Liquid crystals can be composed both of polar and apolar molecules. An important fact in connection with polar substances is that in uniaxial phases there is no polar ordering of the molecules. In average the dipole moments aligned in a given direction are compensated by those aligned in the opposite direction. As a consequence no spontaneous macroscopic polarization develops. More generally one can state that rotation of the director by n does not affect the physical state of the liquid crystal. In biaxial phases built of chiral molecules, such as the chiral smectic C phase, the situation is different. In these systems the compensation of the dipole moments is not perfect, a macroscopic polarization appears in the direction perpendicular both to the layer normal and the director. These phases are therefore ferroelectric. Ferroelectric liquid crystals are currently perhaps the... 

If we limit ourselves to materials without spontaneous macroscopic magnetization, that is M = 0 at zero field, it is easily shown by substituting H = 0 that... 

In the middle diagram of Fig. 5 we have also traced the response for the modification of an antiferroelectric, which we get in the case where the two sublattices have a different polarization size. This phase is designated ferrielectric. Because we have, in this case, a macroscopic polarization, ferrielectrics are a subclass of ferroelectrics. It also has two stable states as it should, although the spontaneous macroscopic polarization is only a fraction of that which can be induced. If the polarization values of the sublattices are F, and P2saturation polarization after sublattice reversal is (F + P2). 

The concentration [MB] constantly experiences tiny fluctuations, the duration of which can determine linewidths. It is also possible to adopt a traditional kinetic viewpoint and measure the time course of such spontaneous fluctuations directly by monitoring the time-varying concentration in an extremely small sample (6). Spontaneous fluctuations obey exactly the same kinetics of return to equiUbrium that describe relaxation of a macroscopic perturbation. Normally, fluctuations are so small they are ignored. The relative ampHtude of a fluctuation is inversely proportional to the square root of the number of AB entities being observed. Consequently, fluctuations are important when concentrations are small or, more usehiUy, when volumes are tiny. 

Another example of the coupling between microscopic and macroscopic properties is the flexo-electric effect in liquid crystals [33] which was first predicted theoretically by Meyer [34] and later observed in MBBA [35], Here orientational deformations of the director give rise to spontaneous polarisation. In nematic materials, the induced polarisation is given by... 

Zhang SG, Holmes T, Lockshin C et al (1993) Spontaneous assembly of a self- complementary oligopeptide to form a stable macroscopic membrane. Proc Natl Acad Sci 90 3334—3338... 

The primary nucleation process is divided into two periods in CNT one is the so called induction period and the other is the steady (or stationary) nucleation period (Fig. 2) [16,17]. It has been proposed by CNT that small (nanometer scale) nuclei will be formed spontaneously by thermal fluctuation after quenching into the supercooled melt, some of the nuclei could grow into a critical nucleus , and some of the critical nuclei will finally survive into macroscopic crystals. The induction period is defined as the period where the nucleation rate (I) increases with time f, whereas the steady period is that where I nearly saturates to a constant rate (fst). It should be noted that I is a function of N and t,I = I(N, t). In Fig. 2, N and N mean the size of a nucleus and that of the critical nucleus, respectively. The size N is defined... 

The spontaneous emergence of structure is a general feature of depositional growth in both natural and technological processes. Macroscopic driving forces, coupled with... 

Electrodeposition of metal onto structured objects, such as circuits, is controlled in part by a template. At the same time, the deposit must fill all the recesses uniformly and seamlessly, the texture and crystal structure must fall within tolerances, and the quality of the features must be sustained over a large workpiece. The distribution of material within recesses or onto widely separated portions of the workpiece is subject to a limited number of macroscopic control-parameters such as applied potential and plating bath composition. Success therefore depends on exploitation of the natural pathways of the process. The spontaneous and unconstrained development of structure must be taken into consideration in the production of highly organized and functional patterns. 

It is noted that all systems in turmoil tend to subside spontaneously to simple states, independent of previous history. It happens when the effects of previously applied external influences damp out and the systems evolve toward states in which their properties are determined by intrinsic factors only. They are called equilibrium states. Experience shows that all equilibrium states are macroscopically completely defined by the internal energy U, the volume V, and the mole numbers Nj of all chemical components. 

For systems close to equilibrium the non-equilibrium behaviour of macroscopic systems is described by linear response theory, which is based on the fluctuation-dissipation theorem. This theorem defines a relationship between rates of relaxation and absorption and the correlation of fluctuations that occur spontaneously at different times in equilibrium systems. 

The relationship between fluctuation and dissipation is reminiscent of the reciprocal Onsager relations that link affinity to flux. The two relationships become identical under Onsager s regression hypothesis which states that the decay of a spontaneous fluctuation in an equilibrium system is indistinguishable from the approach of an undisturbed non-equilibrium system to equilibrium. The conclusion important for statistics, is that the relaxation of macroscopic non-equilibrium disturbances is governed by the same (linear) laws as the regression of spontaneous microscopic fluctuations of an equilibrium system. In the specific example discussed above, the energy fluctuations of a system in contact with a heat bath at temperature T,... 

So far we have considered the formation of tubules in systems of fixed molecular chirality. It is also possible that tubules might form out of membranes that undergo a chiral symmetry-breaking transition, in which they spontaneously break reflection symmetry and select a handedness, even if they are composed of achiral molecules. This symmetry breaking has been seen in bent-core liquid crystals which spontaneously form a liquid conglomerate composed of macroscopic chiral domains of either handedness.194 This topic is extensively discussed in Walba s chapter elsewhere in this volume. Some indications of this effect have also been seen in experiments on self-assembled aggregates.195,196... 

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